Answers
We can further simplify
[tex]\sqrt[]{27}[/tex][tex]\begin{gathered} \sqrt[]{27}\text{ = }\sqrt[]{3\text{ x 9}} \\ \sqrt[]{27}\text{ = }\sqrt[]{3}\text{ x }\sqrt[]{9} \end{gathered}[/tex][tex]\begin{gathered} \sqrt[]{27}\text{ = }\sqrt[]{3}\text{ x 3 = 3 x }\sqrt[]{3} \\ \sqrt[]{27}\text{ = 3 }\sqrt[]{3} \end{gathered}[/tex][tex]\sqrt[]{3}\text{ x }\sqrt[]{27\text{ }}\text{ = }\sqrt[]{3}\text{ x 3}\sqrt[]{3}[/tex]The answers for the blank spaces are
[tex]\sqrt[]{3}\text{ and 3}\sqrt[]{3}[/tex]Related Questions
4to the fitth power times 4 negative 7 expnent
Answers
Answer:
-16,777,216
Step-by-step explanation:
4 to the fifth power =1024
-4 to the seventh power = 16, 384
1024 × -16, 384 =
- 16,777,216
find the coordinates of of the point at -270 degrees on circle radius 3.6 centered at the origin
Answers
Answer: [tex](0, 3.6)[/tex]
Step-by-step explanation:
When rotating -270 degrees, which is the same as 90 degrees, we are going to the topmost point of the graph.
Since the radius is 3.6, this point has coordinates [tex](0, 3.6)[/tex].
A sequence of positive integers with 2020 terms is called an FT sequence if each
term after the second is the sum of the previous two terms. For example, if the
first two terms of an FT sequence are 8 and 7, the sequence would begin
8,7,15, 22, 37,.... For some positive integer m, there are exactly 2415 FT sequences
where the first two terms are each less than 2m and the number of odd-valued
terms is more than twice the number of even-valued terms. What is the value of m?
(A) 21
(B) 69
(C) 115
(D) 35
(E) 105
Answers
The value of m will be 35.
Consider the FT 0, 1, 1, 2, 3, 5, 8, 13, 21, 24,45,.......
The numbers are arranged in order of even, odd, odd, even, odd, odd, even, odd, odd, even,.......
Hence, the loop contains 3 elements. If the number of terms is 2020 terms, then we have 673 loops + 1 element. (That is 3* 673 +1 = 2020) The last element will start the new loop and it is an even number.
In the other hand with 2019 terms, we have number of odd = 2* number of even. But the last term is even. That makes number of odd < twice number of even and it contradicts with the condition.
However in this case, the 2020th term is even and so there are fewer than twice as many odd valued terms as there are even-valued terms.
Thus, there are m2 + m × (m − 1) FT sequences that satisfy the required conditions.
Since there are 2415 such FT sequences, we may solve m2 + m × (m − 1) = 2415 by trial and error.
Evaluating m2 + m × (m − 1) when m = 30, we get 302 + 30 × 29 = 1770, and so m is greater
than 30.
When m = 33, we get 332 + 33 × 32 = 2145.
When m = 34, we get 342 + 34 × 33 = 2278.
When m = 35, we get 352 + 35 × 34 = 2415, as required.
Hence, Answer: (D)
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A rectangle is 4 inches long and 2x inches wide. The value of the perimiter is equal to the value of the area
Answers
When a rectangle has a perimeter equal to the area and is 4 inches long and 2x inches wide, the value of x is 2.
What is the rectangle's perimeter?The sum of the lengths of a rectangle's four sides is referred to as its perimeter.A rectangle's perimeter is equal to 2(L + W).where W denotes the rectangle's width and L denotes its length.GIVEN:
The perimeter (in inches) of a rectangle with dimensions of 4 inches long by 2 inches wide equals the area (in square inches) specified in the question.Rectangle perimeter (P) equals 2x plus 2L.Rectangle area (A) equals LWAs per the stated circumstance,
P = A LW = 2W+2L 2x(4) = 2(2x)+2(4) (4) 8x = 4x +8 4x = 8 x=2HENCE,The value of x is 2 when a rectangle has a perimeter equal to the area, is 4 inches long, and is 2x inches broad.
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3/8 divided by 4/3.5
Answers
1) In this division, we need to turn that decimal number into a fraction:
[tex]undefined[/tex]Select the conic section that represents the equation.3x² + 3y²-2x + 4 = 0
Answers
Given:
[tex]3x^2+3y^2-2x+4=0[/tex]First, we arrange the equation:
[tex]\begin{gathered} 3x^{2}+3y^{2}-2x+4=0 \\ 3x^2-2x+3y^2+4=0 \\ (3x^2-2x)+3y^2=-4 \end{gathered}[/tex]Further simplification of the given equation will give us a result with an imaginary number, making the equation a nonreal circle, or not a conic section.
A gardening shop receives a shipment of 12 crates of plants. Each crate contains 18 plants. A worker displays all the plants on 24 shelves with the same number of plants on each shelf. How many plants are displayed on each shelf?
A. 6
B. 16
C. 9
D. 36
Thanks!
Answers
Answer:16
Step-by-step explanation:
2. The design of the Trieste was based on the design of a hot air balloon built by Auguste Piccard, Jacques's father. In 1932, Auguste rode in his hot-air balloon up to a record-breaking height.A. Auguste's ascent took 7 hours and went up 51,683 feet. Write a relationship y = kx to represent his ascent from his starting location.B. Auguste's descent took 3 hours and went down 52,940 feet. Write another relationship to represent his descent. C. Did Auguste Piccard end up at a greater or lesser altitude than his starting point? How much higher or lower?
Answers
ANSWER
A. y = 7383.3x
B. y = 17646.7x
C. Lesser altitude; 1257 feet
EXPLANATION
A. We want to write a proportional relationship between the time it took him to ascend and the total height he reached:
y = kx
where x = time taken
y = distance (height reached)
k = constant of proportionality
We have to find k for the relationship.
So, we have that:
[tex]\begin{gathered} 51683\text{ = k }\cdot\text{ }7 \\ \Rightarrow\text{ k = }\frac{51683}{7} \\ k\text{ = }7383.3\text{ ft/hr} \end{gathered}[/tex]This constant of proportionality (between distance and time) is called speed.
Therefore, the relationship for his ascent is:
y = 7383.3x
B. For his descent, we also have to find k in:
y = kx
We have that:
[tex]\begin{gathered} 52940\text{ = k }\cdot\text{ 3} \\ k\text{ = }\frac{52940}{3} \\ k=\text{ }17646.7\text{ ft/hr} \end{gathered}[/tex]Therefore, the relationship for his descent is:
y = 17646.7x
C. To find out if he reached a greater or lesser altitude than his starting point, we have to subtract his altitude during ascent from his altitude during descent.
If the value is positive then he ended up at a lesser altitude but if it is negative, he ended up on a greater altitude.
That is:
52940 - 51683
= 1257 feet
Since it is positive, that means that he descended more feet than he ascended and so, he ended up at a lesser altitude than his starting point, 1257 higher.
evaluate the expression 12x-3y when x is -1/4 and y is 3
Answers
Answer:
-12
Step-by-step explanation:
plug in and solve
1. 12(-1/4) - 3(3)
2. -12/4 - 9
3. -3 - 9
4. -12
What is the equation of the line that contains the points ( -1 , 1 ) and ( 5 , -3) ?
Answers
ANSWER:
[tex]y=-\frac{2}{3}x+\frac{1}{3}[/tex]STEP-BY-STEP EXPLANATION:
The equation of the line in its slope and intercept form is as follows:
[tex]\begin{gathered} y=mx+b \\ \text{ where m is the slope and b is y-intercept} \end{gathered}[/tex]The slope can be calculated as follows:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Replacing the points (-1 , 1) and (5 , -3) :
[tex]m=\frac{-3-1}{5-(-1)}=\frac{-4}{5+1}=-\frac{4}{6}=-\frac{2}{3}[/tex]Now, we calculate the value of b, with the help of the slope and the point (-1,1)
[tex]\begin{gathered} 1=-\frac{2}{3}\cdot-1+b \\ b=1-\frac{2}{3} \\ b=\frac{1}{3} \end{gathered}[/tex]Therefore, the equation would be:
[tex]y=-\frac{2}{3}x+\frac{1}{3}[/tex]
pls help this is due today and i have no idea what i am doing
(this isnt math but i didnt see music)
Why is it important for musicians to transcribe music?
Why do you think Beethoven’s story is unique (special)?
What are some ways that we can get better at active listening?
Below is a picture of a musical staff. What is a musical staff? What do the top lines and the bottom lines represent?
an image showing both staffs
What is a musical form? How does it make music more interesting?
Answers
Answer: look at explanation
Step-by-step explanation:
1. It helps you learn and listen to minor details in music better.
2. He had a handicap (partially deaf/deaf) but still managed to overcome and lay his mark in the music world.
3. Pay attention, eye contact, listen, pay attention to nonverbal cues, and show that you are listening
4. A foundation on which notes are drawn on. The lines represent a sound in music. A musical form is the structure of musical compositions. It makes music more interesting because it makes it organized and not jumbled up.
Express the trig ratios as fractions in simplest form.Drop down menu: (a) are equal (b) are not equal
Answers
ANSWER
[tex]\begin{gathered} \sin O=\frac{34}{35} \\ \\ \cos N=\frac{34}{35} \\ \\ \text{ They are equal.} \end{gathered}[/tex]EXPLANATION
We want to express the trigonometric ratios as fractions in the simplest terms.
The trigonometric ratios SOHCAHTOA for right triangles for sine and cosine are:
[tex]\begin{gathered} \sin\theta=\frac{opposite}{hypotenuse} \\ \\ \cos\theta=\frac{adjacent}{hypotenuse} \end{gathered}[/tex]Therefore, for the given triangle, we have that:
[tex]\begin{gathered} \sin O=\frac{34}{35} \\ \\ \cos N=\frac{34}{35} \end{gathered}[/tex]As we see from the equations above, the sine of O and the cosine of N are equal.
Please help me with this question
Answers
Step-by-step explanation:
substitution means to use one equation to express one variable only in terms of the other variable and constants.
let's use
6f + 11b = 317
for that purpose.
6f = 317 - 11b
f = (317 - 11b)/6
now we use that my substituting "f" by its identical expression in b in the second equation :
7(317 - 11b)/6 + 5b = 221
to avoid handling fractions we multiply everything by 6 :
7(317 - 11b) + 30b = 1326
2219 - 77b + 30b = 1326
893 - 47b = 0
893 = 47b
b = 893/47 = 19 cents
f = (317 - 11b)/6 = (317 - 11×19)/6 = (317 - 209)/6 =
= 108/6 = 18 cents
a piece of fudge is 18 cents.
a piece of bubble gum is 19 cents.
points on the coordinate plane below which point would lie on both the x-axis and the y-axis ___thats the question
Answers
We see that the unique point that lie on both the x-axis and the y-axis is the pont (0,0)!
Which function is the inverse of fix) = V5767O A.(-40) =3622 + 2. for = > 0O B.1-1(0) =652 + 2, for = ≥ 0O C.+ 2. for I > 0O D.f-11) = 6522. for r > 0
Answers
Given:
The function is
[tex]f(x)=\frac{\sqrt{x-2}}{6}[/tex]Required:
Find the inverse of the function.
Explanation:
The given function is:
[tex]f(x)=\frac{\sqrt{x-2}}{6}[/tex]Put
[tex]f(x)=y[/tex][tex]y=\frac{\sqrt{x-2}}{6}[/tex]Interchange x and y.
[tex]x=\frac{\sqrt{y-2}}{6}[/tex]Take the square on both sides.
[tex]x^2=\frac{y-2}{36}[/tex][tex]\begin{gathered} 36x^2=y-2 \\ y=36x^2+2 \end{gathered}[/tex]Substitute
[tex]y=f^{-1}(x)[/tex][tex]f^{-1}(x)=36x^2+2[/tex]Final Answer:
Option A is the correct answer.
A student buys 5 books for $47.85. If all of the books are the same price, the cost of each book is
Answers
Answer: $9.57
Step-by-step explanation: 47.85/5 = 9.57. Therefore each book costs $9.57.
What is 4 square root of 4?
Answers
Answer:
8
Step-by-step explanation:
4[tex]\sqrt{4}[/tex]
The [tex]\sqrt{4}[/tex] is 2
4x2 = 8
Answer:The square root of 4 is simply just 2 or in other words, 4 = 2.
Step-by-step explanation:
The value of root 4 is equal to exactly 2. But the roots could be positive or negative or we can say there are always two roots for any given number.
You go on a hayride to take photographs of landmarks. The map shows your path and two landmarks. Each unit in the coordinate plane corresponds to 10 yards. Approximate your minimum distance from the giant pumpkin. If necessary, round your answer to the nearest tenth.
Answers
Using the distance between a point and a line and the conversion of the units to yards, it is found that the minimum distance from the giant pumpkin is of 8.9 yards.
What is the distance between a points and a line?Suppose that we have a linear function defined according to the following rule, in standard notation:
Ax + By + C = 0.
And a point with coordinates given by:
P(x*,y*)
The shortest distance between the line and the point is given by:
[tex]d = \frac{|Ax^\ast + By^\ast + C|}{\sqrt{A^2 + B^2}}[/tex]
The line of the path in this problem has:
Intercept of 0, as when x = 0, y = 0.Slope of 0.5, as when x increases by 4, y increases by 2.Hence:
y = 0.5x.
-0.5x + y = 0
-x + 2y = 0.
The coefficients are:
A = -1, B = 2.
The giant pumpkin has coordinates given by:
(x*, y*) = (-4, -3).
Hence the distance in units is given by:
d = |(-1)(-4) + 2(-3)|/sqrt(5)
d = 2/sqrt(5)
d = 0.89 units.
Each unit is equivalent to 10 yards, hence the shortest distance in yards is given by:
0.89 x 10 = 8.9 yards.
What is the missing information?The problem is given by the image at the end of the answer.
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The answer to which situation is best estimated by -7? How can you estimate decimal amounts?A The temperature falls 1.9°F from 4.3°F.B A hot air balloon rises 4.1 meters from the ground and then rises 2.3 meters more.C A submarine goes 3.8 feet below the surface of the ocean and then goes 2.5 feet farther downD The amount of money Sarah has after she buys milk for $3.85 and bread for $2.45.
Answers
Answer:
C A submarine goes 3.8 feet below the surface of the ocean and then goes 2.5 feet farther down
Explanation:
Option A
[tex]\begin{gathered} 4.3^0F\approx4^0F \\ 1.9^0F\approx2^0F \\ \text{Estimated change in temperature=}4^0F-2^0F=2^0F \end{gathered}[/tex]Option B
[tex]\begin{gathered} 4.1\text{ meters}\approx4\text{ meters} \\ 2.3\text{ meters}\approx2\text{ meters} \\ \text{Estimated change in the balloons's height}=4-2=2\text{ meters} \end{gathered}[/tex]Option C
[tex]\begin{gathered} -3.8f\exponentialE et\approx-4\text{ feet} \\ -2.5f\mathrm{e}et\approx-3\text{ feet} \\ \text{Estimated change in depth=}-4-3=-7\text{ feet} \end{gathered}[/tex]Option D
[tex]\begin{gathered} \$3.85\approx\$4 \\ \$2.45\approx\$2 \\ \text{Change in the amount Sarah has=-}\$4-\$2=-\$6 \end{gathered}[/tex]The situation that is best estimated by -7 is Option C.
6A. Solve h(0)=100-16(0) to the 2nd power and What does the output represent 6B. Solve h(2)=100-16(2) to the 2nd power and does our equation predict that the ball has to hit the ground at 2 seconds. Explain
Answers
I think is confused
6A.- h(0) = 100 - 16(0)^2
= 100 - 0
h(0) = 100
h(0) = 100 ft
The result is the value starting height 100 ft
6B.- h(2) = 100 - 16(2)^2
h(2) = 100 - 64
h(2) = 36 ft
No, the equation does ot predict that the ball is going to hit the ground after 2 seconds because the height was 32 ft, that is the height necessary to hit the ground.
A pool fills up 3 gallons of water in one minute. How many pints does it fill in one minute?
Answers
In this problem we have to use the convertion factor that is equal to 1 so:
[tex]\frac{1gal}{8pn}=1[/tex]so we can made the transormation:
[tex]3\text{gal}\cdot\frac{8pn}{1\text{gal}}=24pn[/tex]So in one minute it fills 24 pints
Mathew deposits 400800.00 kina with the bank which offers 5½% interest per annum. calculate the interest earned after four years if it is compounded annually?
Answers
Solution
For this case we can use the following formula:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]where
A= future value, P= present value= 400800.00
r= 5.5%=0.055, n =1 , t= 4 years
n= represent the number of times that the interest is compounded each year =1 for this case
Replacing we got:
[tex]A=400800\cdot(1+\frac{0.055}{1})^{4\cdot1}=496520.92[/tex]then we can find the interest in the following way:
[tex]I=A-P=496520.92-400800=95720.919[/tex]Sammy is a baker who wants to make profit on his baked goods if it fits him 3.20 or o make a dozen cupcakes how much should he sell them if he wants to make 35% profit
Answers
For there to be a profit,
[tex]\begin{gathered} \\ \text{profit}=\text{ selling price - cost price} \end{gathered}[/tex]From the question,
[tex]\begin{gathered} \text{Cost price = \$3.20} \\ \text{Percentage profit = 35\%} \end{gathered}[/tex]Concept: The formula for the percent profit is given below as
[tex]\text{percentage profit = }\frac{\text{profit}}{\cos t\text{ price}}\times100\text{ \%}[/tex]Given the following information, which is the best description of the data?Range—5, from 12 to 17Mode—14Median—14.5Mean—15The data is around 13.The data is around 12.The data is around 15.The data is around 17.
Answers
we have that
the best description of the data is
The data is around 15The US postal charges $.34 for the 1st ounce and $.23 for each additional ounce. use inequality to find the maximum number of whole ounces that can be mailed for $8.27
Answers
The charges for the first ounce = $0.34
Charges for each additional ounce = $0.23
Let the number of additional ounces be n
The maximum total charges = $8.27
The inequality that represents the given illustration is:
0.34 + 0.23n ≤ 8.27
0.23n ≤ 8.27 - 0.34
0.23n ≤ 7.93
n ≤ 7.93 / 0.23
n ≤ 34.48
Maximum number of whole ounces = Number of additional ouces + Initial ounce
Maximum number of whole ounces = 34.48 + 1
Maximum number of whole ou
Jacob is planting shrubs for a landscaping client. He planted more shrubs in the additional region so that the density of shrubs in the new region is equal to the density of shrubs in the rectangular region as shown.
Answers
ANSWER:
52 shrubs
STEP-BY-STEP EXPLANATION:
We know the number of trees planted in a given area, so to calculate the number of total trees, we must calculate the area of the entire figure and thus calculate by means of a proportion
We calculate the total area if we divide the figure in two, as follows:
The area of zone A, which is a rectangle, is calculated as follows:
[tex]\begin{gathered} A_A=b\cdot h \\ A_A=50\cdot20 \\ A_A=1000 \end{gathered}[/tex]The area of zone B, which is a triangle, is calculated as follows:
[tex]A_B=\frac{b\cdot h}{2}[/tex]To calculate the value of the height of the triangle, we apply the Pythagorean theorem on the right triangle that is formed:
Where the hypotenuse is 25 meters and the other leg is 15 meters, just like this:
[tex]\begin{gathered} h^2=a^2+b^2 \\ 25^2=15^2+b^2 \\ b=\sqrt[]{25^2-15^2} \\ b=\sqrt[]{400} \\ b=20 \\ \text{therefore the height is 20 meters, replacing:} \\ A_B=\frac{30\cdot20}{2} \\ A_B=300 \end{gathered}[/tex]Now, the total area would be the sum of both areas:
[tex]\begin{gathered} A_T=1000+300 \\ A_T=1300 \end{gathered}[/tex]Which means that if in an area of 400 square meters (20 * 20) they can plant 16 shrubs, in an area of 1300 square meters they would be:
[tex]\begin{gathered} \frac{16}{400}=\frac{x}{1300} \\ \text{ solving for x} \\ x=\frac{16\cdot1300}{400} \\ x=52 \end{gathered}[/tex]In other words, a total of 52 shrubs can be raised throughout the region.
What is the slope of the line that passes through the points (4, -2) and (4, 10)?
Write your answer in simplest form.
Answers
The slope of the line that passes through the points (4, -2) and (4, 10) is 0. The slope of a line is 0 if it is horizontal. This function is constant.
What is slope?The ratio of the "vertical change" to the "horizontal change" between (any) two unique points on a line is used to compute slope. The ratio can also be written as a quotient ("rise over run"), which produces the same number for every two distinct points on the same line. A declining line has a negative "rise." The line might be useful, as determined by a road surveyor, or it might appear in a diagram that represents a road or a roof as a description or a design.
The slope's absolute value serves as a gauge for a line's steepness, incline, or grade. A steeper line is indicated by a slope with a higher absolute value. A line can be drawn with one of four directions: upward, downward, horizontal, or vertical.
If a line rises from left to right, it is said to be growing. The slope is upward, or m>0.
If a line slopes downward from left to right, it is diminishing. The slope, m0, is negative.
The slope of a line is 0 if it is horizontal. This function is constant.
A line's slope is ambiguous if it is vertical.
In other terms, the rise is (y2 y1) = y. The rise of a road between two points is the difference in the altitude of the road at those two sites, say y1 and y2. The run, or (x2 x1) = x, is the difference in distance from a given point measured along a level, horizontal line for relatively small distances where the Earth's curvature may be disregarded. Here, the ratio of the altitude change to the horizontal distance between any two places on the line is used to define the slope of the road between the two points.
In mathematical language, slope m of the line is
slope = [tex]\frac{x-x1}{y-y1} =\frac{4-4}{-2+10} = 0[/tex]
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Only about 16% of all people can wiggle their ears. Is this percent different for millionaires? Of the 342 millionaires surveyed, 58 could wiggle their ears. What can be concluded at the α = 0.01 level of significance?For this study, we should use Select an answerThe null and alternative hypotheses would be: H0: ? Select an answer (please enter a decimal) H1: ? Select an answer (Please enter a decimal)The test statistic ? = (please show your answer to 3 decimal places.)The p-value = (Please show your answer to 3 decimal places.)The p-value is ? α Based on this, we should Select an answer the null hypothesis.Thus, the final conclusion is that ...The data suggest the population proportion is not significantly different from 16% at α = 0.01, so there is statistically insignificant evidence to conclude that the population proportion of millionaires who can wiggle their ears is different from 16%.The data suggest the populaton proportion is significantly different from 16% at α = 0.01, so there is statistically significant evidence to conclude that the population proportion of millionaires who can wiggle their ears is different from 16%.The data suggest the population proportion is not significantly different from 16% at α = 0.01, so there is statistically significant evidence to conclude that the population proportion of millionaires who can wiggle their ears is equal to 16%.Part a options:- a. t- test for a population mean- z-test for a population proportionPart b options:(left box): u; ?; p(right box): >; =; =/; >Part c options:t; zPart e options:<; >Part f options:ACCEPT, REJECT, FAIL
Answers
Part a:
In this study, we have only a reference value of 16% (the proportion of people that can wiggle ears) and a population of 342 millionaires whose results we want to compare with this reference value. Since there is a relativelly high number of millionaries that were surveyed, we should use the z-test for a population proportion.
Part b:
It p is the sample proportion, the null hypothesis, in this case, is given by:
[tex]H_0:p=0.16[/tex]Therefore, the alternative hypothesis is given by:
[tex]H_1:p\ne0.16[/tex]Part c:
According to the data, the z-score is given by:
[tex]z=\frac{\frac{58}{342}-\cdot0.16}{\sqrt{\frac{1}{342}\cdot\frac{58}{342}(1-\frac{58}{342})}}\approx0.473[/tex]Part d:
According to the normal table, the p-value related to z-score given by:
0.638
Part e:
Therefore, we can check that this p-value is > a
Part f:
Based on this, we should ACCEPT the null hypothesis.
Part g:
Thus, the final conclusion is that the data suggest the population proportion is not significantly different from 16% at a = 0.01, so there is statistially significant evidence to conclude that the population proportion of millionaries who can wiggle their ears is equal to 16%.
7 John and Raul both bought the same style bike from a store. On
Wednesday, John purchased the bike at a 20% discount off the original
price. On Friday, Raul bought the bike for off the original price.
Part A-Who received the greater discount on the bike? Show your work.
Part B-If John saved $24, what was the original price of the bike? Show
your work.
Use words, numbers and/or pictures to show your work.
Answers
John recieved the greater discount and the original price of the bike is $120
John purchased the bike at a 20% discount off the original
price.
Let the price of the bike be x
The price at which John purchased the bike is x - 20% of x
= x - (20/100)x
=(80/100)x
Raul brought the bike at original price.
Raul's cost price is x
x is greater than (80/100)x
Raul purchased at a greater price than John, so the greater discount is recieved by John.
John got discount = (20/100) x
He saved = $24
(20/100)x = 24
20x =2400
x = 2400/20
x = 120
The original price is $120
Therefore, John recieved the greater discount and the original price of the bike is $120
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State the number of possible real zeros and turning points of f(x) = x^7 – 6x^6 + 8x^5. Then determine all of the real zeros by factoring. 1) 7 real zeros and 6 turning points; 0, 2, and 42) 7 real zeros and 6 turning points; 0, –2, and –43) 6 real zeros and 5 turning points; 0, 2, and 44) 6 real zeros and 5 turning points; 0, –2, and –4
Answers
Step 1
The given equation is
[tex]f(x)=x^7-6x^6+8x^5[/tex]Required: To find the real zeroes by factorization and the turning points.
Step 2
Find the number of real zeroes
[tex]\begin{gathered} x^7-6x^6+8x^5=0 \\ x^5\mleft(x-2\mright)\mleft(x-4\mright)=0 \\ x^5=\text{ 0} \\ x\text{ = 0 five times} \\ ^{}or\text{ } \\ x-2\text{ = 0} \\ x=\text{ 2} \\ or \\ x-4=0 \\ x=\text{ 4} \\ \text{Therefore, there are 7 real zeroes} \end{gathered}[/tex]Step 3
Find the number of turning points.
[tex]f^{\prime}(x)\text{ = }7x^6-36x^5+40x^4[/tex][tex]\begin{gathered} As\text{ se}en\text{ from the differential, the number of turning points is found by subtracting 1 from the highest power of the function.} \\ \text{Hence, the number of turning points = 7-1 = 6} \\ \text{There are 6 turning points} \end{gathered}[/tex]Therefore, there are 7 real zeroes and 6 turning points; 0, 2 and 4
The answer is option A